Compuware holders will receive $10.92 a share, including cash and stock from the spinoff of subsidiary Covisint Corp., representing a premium of about 17 percent to the company’s stock price at the close of trading on Aug. 29, the companies said in a statement Tuesday.

The Detroit-based seller of business software spurned an offer in January 2013 from Elliott Management, which owns 9.6 percent of Compuware. Bob Paul, Compuware’s chief executive officer, cut costs and held an initial public offering of Covisint a year ago. Thoma Bravo had been one of the two firms reviewing the company’s finances in preparation for a possible deal, people with knowledge of the matter said earlier this year. The other potential buyer was Vista Equity Partners LLC.

“Based on how long this has been vetted, and that both the board and Elliott are fully supporting the transaction, we think this is the best offer shareholders are going to get,” Derrick Wood, an analyst at Susquehanna Financial Group LLP, wrote in an e-mail.

According to the terms of the deal, Compuware investors will receive $10.43 in cash for each share. Including a tax charge and a distribution of Covisint shares valued at about 67 cents, they’ll receive a total of $10.92 a share, although that figure may rise depending on a final deal price for Covisint.

The shares of Compuware climbed 13 percent to $10.59 at the close in New York.

Private Company

“Becoming a private company will enable this established market leader to leverage strategic product and other growth opportunities that will take Compuware to the next level,” Orlando Bravo, a managing partner at Thoma Bravo, said in the statement.

Compuware hired Goldman Sachs Group Inc. in 2012 to help it review Elliott’s bid, and the bank also advised on today’s buyout. Elliott made a conditional, non-binding offer to buy the company in 2012 for $11 a share, valuing Compuware at about $2.3 billion. Including dividends paid out since then, Thoma Bravo’s per-share agreement is higher than the earlier Elliott offer.

Jesse Cohn, the portfolio manager at Elliott involved with the Compuware investment, said the company needed to make changes. The deal delivered a 30 percent return for Elliott.